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Carousel Numbers:
A Lead-in to Number Theory

Gary Klatt

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0.     BACKGROUND/OVERVIEW
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PROJECT FOR ALGEBRA AND NUMBER THEORY
COURSE FOR PRE-SERVICE TEACHERS

  -    Ideal for discovery learning
  -    Students work in groups and individually
  -    Uses Derive and custom programs
  -    Students write up results in a paper



FOUR DIVERSE PROBLEMS

  -    Each generates interesting questions and conjectures
  -    3 of the 4 are elementary
  -    Surprising connections to the main problem
  -    Some questions remain open



THE PROBLEMS
  1    CAROUSEL NUMBERS (the appetizer problem)
  2    PERIODS OF DECIMALS (the main problem)
  3    NINE NUMBERS & ONE NUMBERS (useful aside)
  4    GROUP OF UNITS MOD N (final battleground)

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